Topic

About: Hadamard code is a(n) research topic. Over the lifetime, 1049 publication(s) have been published within this topic receiving 12130 citation(s). The topic is also known as: Walsh code & Walsh–Hadamard code.

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Monograph

492 Citations

Open access
01 Jan 1992-

303 Citations

Open accessJournal Article
Abstract: A new code structure for spectral-amplitude-coding optical code-division multiple-access system based on double-weight (DW) code families is proposed. The DW code has a fixed weight of two. By using a mapping technique, codes that have a larger number of weights can be developed. Modified double-weight (MDW) code is a DW code family variation that has variable weights of greater than two. The newly proposed code possesses ideal cross-correlation properties and exists for every natural number n. Based on theoretical analysis and simulation, MDW code is shown here to provide a much better performance compared to Hadamard and modified frequency-hopping codes.

Topics: Constant-weight code (72%), Systematic code (69%), Polynomial code (69%) ...read more

274 Citations

Open accessJournal Article
Abstract: Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,..., 16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12,14 and 16, which we could not find in the existing literature.

273 Citations

Open accessJournal Article
Abstract: An $n \times n$ matrix $H$ with all its entries $+1$ and $-1$ is Hadamard if $HH' = nI$. It is well known that $n$ must be 1, 2 or a multiple of 4 for such a matrix to exist, but is not known whether Hadamard matrices exist for every $n$ which is a multiple of 4. The smallest order for which a Hadamard matrix has not been constructed is (as of 1977) 268. Research in the area of Hadamard matrices and their applications has steadily and rapidly grown, especially during the last three decades. These matrices can be transformed to produce incomplete block designs, $t$-designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III designs, optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects. In this paper we survey the existence of Hadamard matrices and many of their applications.

272 Citations

##### Performance
###### Metrics
No. of papers in the topic in previous years
YearPapers
202112
202011
201927
201817
201719
201633

###### Top Attributes

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Topic's top 5 most impactful authors

Christos Koukouvinos

9 papers, 120 citations

5 papers, 119 citations

Hakob Sarukhanyan

5 papers, 12 citations

Ali N. Akansu

5 papers, 19 citations

Martin Bossert

4 papers, 29 citations

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